Transmitter finite impulse response characterization

ABSTRACT

A finite impulse response (FIR) extractor includes at least one controller. The controller injects specified FIR tap values into a first captured waveform that results from transmitting a raw waveform through a transmitter circuit including a FIR filter having pre and post cursor tap values set to zero to create an expected waveform, and injects the specified FIR tap values into the raw waveform to create an ideal waveform. The controller further projects the expected and ideal waveforms onto a second captured waveform that results from transmitting the ideal waveform through the transmitter circuit with the pre and post cursor tap values set to the specified FIR tap values to create a compensated waveform, and extracts FIR tap values from the compensated waveform.

TECHNICAL FIELD

This disclosure relates to high-speed transmitter characterization.

BACKGROUND

In signal processing, a finite impulse response (FIR) filter has animpulse response of finite duration. Infinite impulse response (IIR)filters, in contrast, may have internal feedback and may continue torespond indefinitely.

FIR filters may have several useful properties: (a) They require nofeedback. Hence, rounding errors are not compounded by summediterations. The same relative error occurs in each calculation. (b) Theyare inherently stable. Because there is no required feedback, all polesare located at the origin and thus within the unit circle. (c) They canbe designed to have linear phase (or phase change proportional tofrequency) by setting the coefficient sequence to be symmetric. Such maybe desirable for phase-sensitive applications such as datacommunications, crossover filters, and mastering.

SUMMARY

Estimating finite impulse response (FIR) of a FIR filter includesinjecting specified FIR tap values into a first captured waveform thatresults from transmitting a raw waveform through a transmitter circuitincluding the FIR filter having pre and post cursor tap values set tozero to create an expected waveform, and injecting the specified FIR tapvalues into the raw waveform to create an ideal waveform. Estimating theFIR further includes projecting the expected and ideal waveforms onto asecond captured waveform that results from transmitting the idealwaveform through the transmitter circuit with the pre and post cursortap values set to the specified FIR tap values to create a compensatedwaveform, and extracting FIR tap values from the compensated waveform.Estimating the FIR may further include extracting a cursor tap valuefrom the second captured waveform. Extracting FIR tap values from thecompensated waveform may include aligning the compensated and idealwaveforms in time. Injecting specified FIR tap values into a firstcaptured waveform may include convolving the specified FIR tap valuesand first captured waveform. Injecting the specified FIR tap values intothe raw waveform may include convolving the FIR tap values and rawwaveform. Projecting the expected and ideal waveforms onto a secondcaptured waveform may include taking the product of the second capturedwaveform and the quotient of the ideal and expected waveforms. The rawwaveform may be a repeating waveform.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot of finite impulse response (FIR) taps.

FIG. 2 is a plot of the pulse response of FIG. 1.

FIG. 3 is a plot of the pulse response calculated from the impulseresponse Fast Fourier transform method for a PRBS7 pattern.

FIG. 4 is a flow chart of an algorithm for characterizing FIR output.

FIG. 5 is a plot of a bandwidth limited eight-ones-eight-zeros patterncontrasted with an ideal pattern, which is not bandwidth limited.

FIG. 6 is a plot of no-FIR compensated and ideal waveforms.

FIG. 7 is a plot of measured, idealistic and ideal waveforms.

FIG. 8 is a plot of FIR compensated and ideal waveforms.

DETAILED DESCRIPTION

Embodiments of the present disclosure are described herein. It is to beunderstood, however, that the disclosed embodiments are merely examplesand other embodiments can take various and alternative forms. Thefigures are not necessarily to scale; some features could be exaggeratedor minimized to show details of particular components. Therefore,specific structural and functional details disclosed herein are not tobe interpreted as limiting, but merely as a representative basis forteaching one skilled in the art to variously employ the presentinvention. As those of ordinary skill in the art will understand,various features illustrated and described with reference to any one ofthe figures can be combined with features illustrated in one or moreother figures to produce embodiments that are not explicitly illustratedor described. The combinations of features illustrated providerepresentative embodiments for typical applications. Variouscombinations and modifications of the features consistent with theteachings of this disclosure, however, could be desired for particularapplications or implementations.

In many high speed signal applications, finite impulse response (FIR)pre-compensation is necessary to improve signal integrity and preventdata corruption. Thus, characterizing the FIR output of a transmitterincluding a FIR filter may become important in design. Accuratelymeasuring the FIR at the output is problematic when there are lossymicrostrips, striplines, cables, connectors, and other transmissionlines needed to connect the output of the transmitter to a scope. Theselossy transmission lines cause undesired distortions in the signal,effectively misshaping it such that the FIR measured at the scope doesnot reflect the true FIR transmitter output.

Certain algorithms described herein may compensate for the bandwidthlimitations of the FIR measurement by, for example, computing theconvolved FIR tap values from a waveform with no FIR, dividing theresultant convoluted waveform from the measured waveform, andmultiplying it by the ideal waveform. This could be implemented as afeature on a machine (scope) that can be enabled with, for example, thepush of a button that would then extract the FIR taps and transpose themonto the ideal waveform.

FIR Basics

The output, y′, of a linear time invariant system is determined byconvolving its input signal, y, with its impulse response, h:

y′=y*h  (1)

This is the simplest form of a FIR. The impulse response, h, can besomething other than unity and is known as the cursor height. (Changingthis height can be used to set transmitter output swing values.)

Generally, FIR can be represented as a series of δ functions:

h=δ·pre_(x-1)+ . . . +δ·pre₁+δ·cur+δpst_(x-1)+ . . . +δ·pst_(x)  (2)

where

y=δ*y  (3)

and the numbered positions of pre and pst are the FIR cursor taps. Theposition of these taps corresponds to the transition regions in which alogical “1” changes to a logical “0” and a logical “0” changes to alogical “1.” (FIR affects only the fast transitional states and not thestable low-frequency regions.)

(3) may be simplified to

h=δ(t+1_([UI]))·pre₁+δ(t)·cur+δ(t−1_([UI]))·pst₁  (4)

which is graphically depicted in FIG. 1. It is often difficult toextract the tap values when in the form shown in FIG. 1. In practicewhen in this form, the waveform is usually convolved with a unity pulsehaving a width of 1 UI as shown in FIG. 2.

The flat stable regions illustrated in FIG. 2 are the exact tap heightsin an ideal case and can be easily measured. (If either the systemimpulse response or the system pulse response is known, the FIR taps canbe extracted.) As mentioned previously, this form is preferred inpractice since under non-ideal conditions the resolution is notsufficient to yield fast rise and fall transition times. Furthermore,computational statistical error is present in the resultant output.

Characterizing FIR Output—Traditional Techniques

One of two methodologies is typically used to characterize and measurethe FIR output. The first technique de-embeds the transmission lines bymeasuring the S-parameter of the undesired cables and traces. This canbe realized by dividing the Fast Fourier transform (FFT) of the measuredwaveform, y_([measured]), by the insertion loss portion of theS-parameter, S₂₁. An inverse Fast Fourier transform (IFFT) of the resultyields the de-convolved waveform, y_([de-embedded]). This can berepresented as

$\begin{matrix}{y_{\lbrack{{de}\text{-}{embedded}}\rbrack} = {{IFFT}\left\{ \frac{{FFT}\left\{ y_{\lbrack{measured}\rbrack} \right\}}{S_{21}} \right\}}} & (5)\end{matrix}$

It, however, can be difficult to accurately measure the S-parameterbecause there is often no way to access the exact traces and connectors,there is no way to isolate the traces causing undesired capacitances,and the probes used to measure the traces produce undesired interferencewith the measurement. Also, there are other loss components that cannotbe accounted for in the S-parameter measurement. These include thebandwidth limitations of the transmitter circuitry itself: Thetransmitter circuitry is composed of capacitors, inductors, traces,etc., and each has a bandwidth limitation and corresponding lossprofile. Such is inherent to the circuit design and cannot be removedwith a S-parameter measurement.

In order to characterize inaccessible traces, designers may include teststructures that mimic these traces. These test structures are arepresentation of what the actual transmission line should be and aredesigned to facilitate S-parameter measurements. The obvious dilemma isthat in these cases one may not have an accurate measurement/model ofthe S-parameter which may invalidate the FIR de-embedded waveform.

The second technique to measure and characterize FIR output attempts tocompensate for the bandwidth by measuring a pattern waveform of largetransitional states with and without FIR. This method divides the FFT ofthe waveform with FIR, y_([with FIR]), by the FFT of the waveformwithout FIR, y_([no FIR]). An IFFT of the result is the system impulseresponse, h_([de-embedded]). This can be represented as

$\begin{matrix}{h_{\lbrack{{de}\text{-}{embedded}}\rbrack} = {{IFFT}\left\{ \frac{{FFT}\left\{ y_{\lbrack{{with}\mspace{11mu} {FIR}}\rbrack} \right\}}{{FFT}\left\{ y_{\lbrack{{no}\mspace{11mu} {FIR}}\rbrack} \right\}} \right\}}} & (6)\end{matrix}$

Convolving the system impulse response with a pulse of 1 UI yields theFIR tap settings.

This second technique has several benefits: (a) All of the taps can beextracted. (b) The traces, connectors, etc. in both captured waveformsare measured. (c) Since the waveforms are divided in the frequencydomain, the impulse response only contains the FIR. (d) No teststructures or S-parameter measurements are needed.

There are also, however, several drawbacks: (a) Patterns containing manytransitional states are necessary. This is driven by the FFT algorithm.Essentially, the FFT is a numerical approximation that attempts toapproximate the Fourier equivalent of the harmonics of the waveform.Hence, many transitional states are needed to provide sufficientresolution for a clean measurement. (b) A relatively long time is neededto achieve good resolution. Many transitional states require a largerpattern waveform. In practice, a PRBS7 waveform (127 bits) is necessaryfor acceptable resolution, although a PRBS15 waveform (2¹⁵−1 bits)yields much better results. FIG. 3 shows the results using a PRBS7pattern. The slower rise and fall transition times are not caused bybandwidth limitations. Rather, they result from lower resolution frominsufficient transition states. Capturing a larger PRBS pattern mayyield faster rise time edges that are closer to ideal. It takes secondsto capture a PRBS7 pattern from a sampling scope whereas it takesminutes to capture a PRBS15 waveform from the same scope. (c) The FFTalgorithm introduces noise into the results. (d) There is nodifferentiation in the FIR tap values between the rising and fallingedges.

Characterizing FIR Output—Bandwidth Compensation Technique

Algorithms for characterizing and measuring FIR output that may besimpler, faster, and cheaper than other viable methods are disclosedherein. Furthermore, these algorithms can be implemented into thesoftware of currently existing scopes and may provide a graphical userinterface that displays the swing and FIR values for an ideal waveform(infinite bandwidth), an “idealistic” waveform (expected waveform basedon tap values), and the measured waveform. Additional displays mayinclude a display of the compensated waveform (bandwidth limitationsremoved) and the ideal waveform.

In the following example, a repeating eight-ones-eight-zeros pattern,y_([raw]), is used with an oversampling rate of 32 points per bit. Thispattern consists of eight logic level “1's” for the first eight bits andeight logic level “0's” for the last eight bits. The total patternlength is 16 bits and repeats after the 16^(th) bit. The algorithmsdescribed herein, however, will work with any size waveform pattern andare not limited to the eight-ones-eight-zeros pattern. The pattern ofthe following example was chosen for reasons related to simplicity andspeed since it provides a minimum number of transitional states (riseand fall) with long stable regions in which capacitors can saturate andreach steady state. Furthermore, any transmitter with FIR should be ableto transmit such a pattern or one similar.

With reference to FIG. 4, a controller (or controllers) 10 isoperatively arranged with a display 12 and a transmitter circuit 14including a FIR filter 16. At operation 18, an ideal waveform,y_([ideal]), which has infinite bandwidth, is calculated at operation 10by convolving (injecting) the eight-ones-eight-zeros pattern, y_([raw]),with specified FIR tap values, h_([FIR taps]). This can be representedas

y _([ideal]) =y _([raw]) *h _([FIR taps])  (7)

The results resemble a clean square pulse (see e.g., FIG. 5), in whichthe transition region is very short—corresponding to the fastest riseand fall times possible.

At operation 20, the eight-ones-eight-zeros waveform is measured withoutFIR under “best case” conditions including all connectors, traces, etc.That is, the eight-ones-eight-zeros waveform is transmitted through thetransmitter circuit 14 including the FIR filter 16 with its pre and postcursor tap values set to zero, and the resulting output, y_([no FIR]),is then captured. This “best case” measurement of no FIR is a baselinemeasurement and contains all of the bandwidth information.

At operation 22, the FIR present is computed by convolving themeasurement from operation 20 with the FIR tap values. This can berepresented as

y _([idealistic]) =y _([no FIR]) *h _([FIR taps])  (8)

The resultant convolved waveform, y_([idealistic]), is the “idealistic”or expected waveform.

At operation 24, the waveforms are aligned such that the first eight“0's” of the measured waveform correlates to the first eight “0's” ofthe “idealistic” waveform. At operation 26, the ideal and “idealistic”waveforms are scaled to the measured waveform height. Care should betaken when scaling to ensure that singularities are removed. Thus inmany instances, the waveforms should be shifted away from any zeropoints. Otherwise, division by zero is possible—resulting in artifacts.

At operation 28, the measured, “idealistic,” and ideal waveforms aresuperimposed onto one another according to user preference. With no FIRpresent, the “idealistic” and measured waveforms overlay each other asshown in FIG. 5. The transitional regions of the measured waveformextend across the neighboring bits. This is because the pre and postcursor tap values are zero, leaving only the cursor, which simplysamples the measured waveform according to (1). FIG. 6 illustrates howthe plot may appear for the case in which there is no FIR. Theidealistic and measured waveforms overlay when compensated showing thatthey are the same. FIGS. 7 and 8 illustrate examples of how other plotswith FIR may appear. The difference between the idealistic and measuredwaveforms reveals the FIR. Without computing the difference, erroneousvalues may be extracted for the FIR tap values as illustrated. The plotin this step can be scaled (transformed) to a FIR scale or to themeasured volts scale. In FIGS. 5 through 8, the waveforms are alignedand displayed such that four “0's” are first, followed by eight “1 's,”then the remaining four “0's.” In certain examples, the waveformalignment can be adjustable so that the user may change or correct it asdesired.

At operation 30, the eight-ones-eight-zeros waveform is measured withFIR. That is, the eight-ones-eight-zeros waveform is transmitted throughthe transmitter circuit 14 including the FIR filter 16 with its pre andpost cursor tap values set to the specified tap values, and theresulting output, y_([FIR]), is then captured.

At operation 32, the FIR compensation waveform, y_([compensated]), iscalculated by taking the product of the waveform measured at operation30 and the quotient of the ideal and “idealistic” waveforms. This can berealized by the linear algebra transformation

$\begin{matrix}{y_{\lbrack{compensated}\rbrack} = {\frac{y_{\lbrack{ideal}\rbrack}}{y_{\lbrack{idealistic}\rbrack}}{xy}_{\lbrack{FIR}\rbrack}}} & (9)\end{matrix}$

which projects the “idealistic” and ideal FIR waveforms onto thecaptured FIR waveform—thus removing the bandwidth components. Thistransforms the measured FIR waveform to the “ideal” vector space. (The“idealistic” and measured waveforms are in the same vector space. Hence,this is a valid way to transform the measured FIR to the “ideal” vectorspace.)

At operation 34, the compensated and ideal waveforms are superimposed onthe same plot such that the FIR tap values of the compensated waveformand the FIR tap values of the ideal FIR waveform are aligned in time.This allows a direct comparison and extraction of the FIR tap values.FIG. 8 is an example of how the plots may appear. The compensated FIR isdisplayed with the ideal waveform. When compensated, effects of limitedbandwidth are removed from the eight-ones-eight-zeroes pattern. Thisdisplay can be scaled to a FIR scale or to the measured volts scale.

At operation 36, the FIR tap heights (cursor height optional) areextracted and displayed on the plots. Various known algorithms may beused and may vary depending on the user defined pattern sent. In thecase of the eight-ones-eight-zeros pattern, the measurements areaveraged in the regions where the taps manifest. Additionally, the swingheight can be measured and displayed. Measurements of the swing heightmay become important since changes to the FIR taps directly affect theswing height. Current methods may specify only voltage peak-to-peakvalues with a specific FIR setting, which can be different depending onthe circuit specifications.

At operation 38, operations 18 through 36 may be used to iterativelycalculate the FIR tap values and the cursor value/swing height from themeasured waveform. Under testing conditions, the FIR taps are known anda direct comparison of the measured values of the taps heights istypically most useful. There may be testing scenarios, however, in whichthe cursor height is not known. In such cases, the iterative process inthis step will extract all the tap values. The iteration should havebounded values that are user defined and will select the values with thebest fit for the FIR taps. Assuming user defined bounded values for thecursor of 0 and 1, for example, the pre-cursor tap and post-cursor tapvalues would be best fit adjusted against the measured waveform for eachof the cursor values. The best fit waveform having the least error(least squared error) relative to the measured waveform yields the FIRtap values and the cursor value/swing height.

There may be several advantages to using the algorithms described above:(a) No S-parameter measurement is necessary. Instead, the signal of thesystem is used to compensate for the bandwidth. (b) There is no need fortest structures since the measurements from the exact transmission linesare used. (c) An expected “idealistic” waveform is provided. (d) The FIRtap values for the rising and falling edges are provided. (e) Simplewaveforms can be measured. Hence, these algorithms are not limited tolarge transitional waveform patterns, e.g. PRBS7. (f) These techniquescan be used to accurately measure the swing of a waveform with FIR.Extreme FIR values distort the waveform such that simple voltagepeak-to-peak measurements are either meaningless or invalid. Thesetechniques can be used to correlate an ideal to the “idealistic” andmeasured waveforms to accurately extract meaningful swing values. (g)These algorithms may be fast since smaller patterns can be used insteadof patterns with a larger number of transitional states. (h) The FIR maybe plotted in easy to understand diagrams of the waveform pattern andthe compensated waveform. Although the cursor and FIR taps should beknown, they can be determined by running an iteration that finds thebest fit for the FIR taps as mentioned with reference to operation 38.

The algorithms disclosed herein may facilitate two new displays: one forsuperimposed plots of the ideal, “idealistic,” and measured FIRwaveforms, and a second for superimposed plots of the compensated andideal waveforms. These techniques may also provide useful informationfor FIR design and characterization, and provide means to extract FIRmeasurements without bandwidth limitation. These algorithms can beimplemented into an existing scope's software to increase themeasurement functionality and value of the scope.

The processes, methods, or algorithms disclosed herein can bedeliverable to/implemented by a processing device, controller, orcomputer, which can include any existing programmable electronic controlunit or dedicated electronic control unit. Similarly, the processes,methods, or algorithms can be stored as data and instructions executableby a controller or computer in many forms including, but not limited to,information permanently stored on non-writable storage media such as ROMdevices and information alterably stored on writeable storage media suchas floppy disks, magnetic tapes, CDs, RAM devices, and other magneticand optical media. The processes, methods, or algorithms can also beimplemented in a software executable object. Alternatively, theprocesses, methods, or algorithms can be embodied in whole or in partusing suitable hardware components, such as Application SpecificIntegrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs),state machines, controllers or other hardware components or devices, ora combination of hardware, software and firmware components.

While exemplary embodiments are described above, it is not intended thatthese embodiments describe all possible forms encompassed by the claims.The words used in the specification are words of description rather thanlimitation, and it is understood that various changes may be madewithout departing from the spirit and scope of the disclosure. Aspreviously described, the features of various embodiments can becombined to form further embodiments of the invention that may not beexplicitly described or illustrated. While various embodiments couldhave been described as providing advantages or being preferred overother embodiments or prior art implementations with respect to one ormore desired characteristics, those of ordinary skill in the artrecognize that one or more features or characteristics can becompromised to achieve desired overall system attributes, which dependon the specific application and implementation. These attributes mayinclude, but are not limited to cost, strength, durability, life cyclecost, marketability, appearance, packaging, size, serviceability,weight, manufacturability, ease of assembly, etc. As such, embodimentsdescribed as less desirable than other embodiments or prior artimplementations with respect to one or more characteristics are notoutside the scope of the disclosure and can be desirable for particularapplications.

What is claimed is:
 1. A method for estimating finite impulse response(FIR) of a FIR filter, the method comprising: by at least onecontroller, injecting specified FIR tap values into a first capturedwaveform that results from transmitting a raw waveform through atransmitter circuit including the FIR filter having pre and post cursortap values set to zero to create an expected waveform, injecting thespecified FIR tap values into the raw waveform to create an idealwaveform, projecting the expected and ideal waveforms onto a secondcaptured waveform that results from transmitting the ideal waveformthrough the transmitter circuit with the pre and post cursor tap valuesset to the specified FIR tap values to create a compensated waveform,and extracting FIR tap values from the compensated waveform.
 2. Themethod of claim 1 wherein extracting FIR tap values from the compensatedwaveform includes aligning the compensated and ideal waveforms in time.3. The method of claim 1 wherein injecting specified FIR tap values intoa first captured waveform includes convolving the specified FIR tapvalues and the first captured waveform.
 4. The method of claim 1 whereininjecting the specified FIR tap values into the raw waveform includesconvolving the FIR tap values and the raw waveform.
 5. The method ofclaim 1 wherein projecting the expected and ideal waveforms onto asecond captured waveform includes taking the product of the secondcaptured waveform and the quotient of the ideal and expected waveforms.6. The method of claim 1 further comprising extracting a cursor tapvalue from the second captured waveform.
 7. The method of claim 1wherein the raw waveform is a repeating waveform.
 8. A finite impulseresponse (FIR) extractor comprising: at least one controller programmedto inject specified FIR tap values into a first captured waveform thatresults from transmitting a raw waveform through a transmitter circuitincluding a FIR filter having pre and post cursor tap values set to zeroto create an expected waveform, inject the specified FIR tap values intothe raw waveform to create an ideal waveform, project the expected andideal waveforms onto a second captured waveform that results fromtransmitting the ideal waveform through the transmitter circuit with thepre and post cursor tap values set to the specified FIR tap values tocreate a compensated waveform, and extract FIR tap values from thecompensated waveform.
 9. The extractor of claim 8 wherein extracting FIRtap values from the compensated waveform includes aligning thecompensated and ideal waveforms in time.
 10. The extractor of claim 8wherein injecting specified FIR tap values into a first capturedwaveform includes convolving the specified FIR tap values and the firstcaptured waveform.
 11. The extractor of claim 8 wherein injecting thespecified FIR tap values into the raw waveform includes convolving theFIR tap values and the raw waveform.
 12. The extractor of claim 8wherein projecting the expected and ideal waveforms onto a secondcaptured waveform includes taking the product of the second capturedwaveform and the quotient of the ideal and expected waveforms.
 13. Theextractor of claim 8 wherein the at least one controller is furtherprogrammed to extract a cursor tap value from the second capturedwaveform.
 14. The extractor of claim 8 wherein the at least onecontroller is further programmed to provide output indicative of thecompensated and ideal waveforms for display.
 15. The extractor of claim8 wherein the raw waveform is a repeating waveform.
 16. Acomputer-readable storage medium having instructions stored thereonthat, when executed by a processor, cause the processor to injectspecified finite impulse response (FIR) tap values into a first capturedwaveform that results from transmitting a raw waveform through atransmitter circuit including a FIR filter having pre and post cursortap values set to zero to create an expected waveform, inject thespecified FIR tap values into the raw waveform to create an idealwaveform, project the expected and ideal waveforms onto a secondcaptured waveform that results from transmitting the ideal waveformthrough the transmitter circuit with the pre and post cursor tap valuesset to the specified FIR tap values to create a compensated waveform,and extract FIR tap values from the compensated waveform.
 17. The mediumof claim 16 wherein extracting FIR tap values from the compensatedwaveform further includes aligning the compensated and ideal waveformsin time.
 18. The medium of claim 16 wherein injecting specified FIR tapvalues into a first captured waveform includes convolving the specifiedFIR tap values and the first captured waveform.
 19. The medium of claim16 wherein injecting the specified FIR tap values into the raw waveformincludes convolving the FIR tap values and the raw waveform.